EXAMPLE 1 Use the substitution method

Solve the linear system:

y = 3x + 2

Equation 2

Equation 1

x + 2y = 11

Solve for y. Equation 1 is already solved for y.

SOLUTION

STEP 1

EXAMPLE 1 Use the substitution method

7x + 4 = 11 Simplify.

7x = 7 Subtract 4 from each side.

x = 1 Divide each side by 7.

Substitute 3x + 2 for y.x + 2(3x + 2) = 11

Write Equation 2.x + 2y = 11

Substitute 3x + 2 for y in Equation 2 and solve for x.

STEP 2

EXAMPLE 1 Use the substitution method

ANSWER

The solution is (1, 5).

Substitute 1 for x in the original Equation 1 to find the value of y.

y = 3x + 2 = 3(1) + 2 = 3 + 2 = 5

STEP 3

GUIDED PRACTICE

CHECK

y = 3x + 2

5 = 3(1) + 2?

5 = 5

Substitute 1 for x and 5 for y in each of the original equations.

x + 2y = 11

1 + 2 (5) = 11?

11 = 11

EXAMPLE 1 Use the substitution method

EXAMPLE 2 Use the substitution method

Solve the linear system:x – 2y = –6 Equation 1

4x + 6y = 4 Equation 2SOLUTION

Solve Equation 1 for x.

x – 2y = –6 Write original Equation 1.

x = 2y – 6 Revised Equation 1

STEP 1

EXAMPLE 2 Use the substitution method

Substitute 2y – 6 for x in Equation 2 and solve for y.

4x + 6y = 4 Write Equation 2.

4(2y – 6) + 6y = 4 Substitute 2y – 6 for x.

Distributive property8y – 24 + 6y = 4

14y – 24 = 4 Simplify.

14y = 28 Add 24 to each side.

y = 2 Divide each side by 14.

STEP 2

EXAMPLE 2 Use the substitution method

Substitute 2 for y in the revised Equation 1 to find the value of x.

x = 2y – 6 Revised Equation 1

x = 2(2) – 6 Substitute 2 for y.

x = –2 Simplify.

ANSWER The solution is (–2, 2).

STEP 3

4(–2) + 6 (2) = 4 ?

GUIDED PRACTICE

CHECK

–2 – 2(2) = –6?

–6 = –6

Substitute –2 for x and 2 for y in each of the original equations.

4x + 6y = 4

4 = 4

Equation 1 Equation 2

x – 2y = –6

EXAMPLE 2 Use the substitution method

EXAMPLE 1 Use the substitution method

Solve the linear system using the substitution method.

3x + y = 10

y = 2x + 51.

GUIDED PRACTICE for Examples 1 and 2

ANSWER (1, 7)

EXAMPLE 2 Use the substitution method

x + 2y = –6

GUIDED PRACTICE for Examples 1 and 2

x – y = 32.

ANSWER (0, –3)

Solve the linear system using the substitution method.

EXAMPLE 2 Use the substitution method

–2x + 4y = 0

GUIDED PRACTICE for Examples 1 and 2

3x + y = –73.

Solve the linear system using the substitution method.

ANSWER (–2, –1)